The multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wavefunction with nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.\

},
doi = {https://doi.org/10.1103/PhysRevLett.122.120502},
url = {https://arxiv.org/abs/1807.11486},
author = {Su-Kuan Chu and Guanyu Zhu and James R. Garrison and Zachary Eldredge and Ana Vald{\'e}s Curiel and Przemyslaw Bienias and I. B. Spielman and Alexey V. Gorshkov}
}
@article {1412,
title = {Chern numbers hiding in time-of-flight images},
journal = {Physical Review A},
volume = {84},
year = {2011},
month = {2011/12/21},
abstract = { We present a technique for detecting topological invariants -- Chern numbers
-- from time-of-flight images of ultra-cold atoms. We show that the Chern
numbers of integer quantum Hall states of lattice fermions leave their
fingerprints in the atoms{\textquoteright} momentum distribution. We analytically demonstrate
that the number of local maxima in the momentum distribution is equal to the
Chern number in two limiting cases, for large hopping anisotropy and in the
continuum limit. In addition, our numerical simulations beyond these two limits
show that these local maxima persist for a range of parameters. Thus, an
everyday observable in cold atom experiments can serve as a useful tool to
characterize and visualize quantum states with non-trivial topology.
},
doi = {10.1103/PhysRevA.84.063629},
url = {http://arxiv.org/abs/1105.3100v3},
author = {Erhai Zhao and Noah Bray-Ali and Carl J. Williams and I. B. Spielman and Indubala I. Satija}
}